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Neural Networks (NNs) can provide major empirical performance improvements for robotic systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating the…

Computational Fluid Dynamics (CFD) simulations are often constrained by the memory-bound nature of sparse matrix-vector operations, which eventually limits performance on modern high-performance computing (HPC) systems. This work introduces…

In this paper, we present Gauss's law-preserving spectral methods and their efficient solution algorithms for curl-curl source and eigenvalue problems in two and three dimensions arising from Maxwell's equations. Arbitrary order…

This work addresses integrating probabilistic propositional logic constraints into the distribution encoded by a probabilistic circuit (PC). PCs are a class of tractable models that allow efficient computations (such as conditional and…

The task of recovering a low-rank matrix from its noisy linear measurements plays a central role in computational science. Smooth formulations of the problem often exhibit an undesirable phenomenon: the condition number, classically…

The present paper studies a kind of robust optimization problems with constraint. The problem is formulated through Backward Stochastic Differential Equations (BSDEs) with quadratic generators. A necessary condition is established for the…

We propose two efficient numerical approaches for solving variable-order fractional optimal control-affine problems. The variable-order fractional derivative is considered in the Caputo sense, which together with the Riemann-Liouville…

We introduce COLOSS, a program designed to address the scattering problem using a bound-state technique known as complex scaling. In this method, the oscillatory boundary conditions of the wave function are transformed into exponentially…

Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…

In distributed machine learning, a central node outsources computationally expensive calculations to external worker nodes. The properties of optimization procedures like stochastic gradient descent (SGD) can be leveraged to mitigate the…

Binary embedding of high-dimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To…

The conventional rounding error analysis provides worst-case bounds with an associated failure probability and ignores the statistical property of the rounding errors. In this paper, we develop a new statistical rounding error analysis for…

We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…

Coded distributed computing was recently introduced to mitigate the effect of stragglers on distributed computing. This paper combines ideas of approximate computing with coded computing to further accelerate computation. We propose…

Binary embedding is the problem of mapping points from a high-dimensional space to a Hamming cube in lower dimension while preserving pairwise distances. An efficient way to accomplish this is to make use of fast embedding techniques…

In this paper, we study stochastic submodular maximization problems with general matroid constraints, that naturally arise in online learning, team formation, facility location, influence maximization, active learning and sensing objective…

In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…

We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63--72]. As a…

This study presents the derivation of a recursive formula for integrals of products of $N$ Hermite polynomials, establishing a numerically stable scheme for their accurate evaluation in computer codes. The derivation is notably simple and…

Maximum distance separable (MDS) array codes constitute an important class of error-correcting codes due to their optimal distance properties and their relevance in distributed storage systems. In this paper, we investigate the construction…